Obviously, the eigenvalues of are . Let be the identity matrix and consider , by direct computation, you see that . These data say the following:
the number of Jordan blocks of at least size 1= =4-2=2
the number of Jordan blocks of at least size 2= =2-1=1
the number of Jordan blocks of at least size 3= =1-0=1
the number of Jordan blocks of at least size 4= =0
So the Jordan form of is and hence the Jordan form of is .

I don't understand the definition of "Jordan basis", could you tell me?